Temat: weakly connected domination number - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Weakly connected domination subdivision numbers
Autorzy:: Raczek, Joanna
Powiązania:: https://bibliotekanauki.pl/articles/743529.pdf
Data publikacji:: 2008
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: weakly connected domination number
weakly connected domination subdivision number
Opis:: A set D of vertices in a graph G = (V,E) is a weakly connected dominating set of G if D is dominating in G and the subgraph weakly induced by D is connected. The weakly connected domination number of G is the minimum cardinality of a weakly connected dominating set of G. The weakly connected domination subdivision number of a connected graph G is the minimum number of edges that must be subdivided (where each egde can be subdivided at most once) in order to increase the weakly connected domination number. We study the weakly connected domination subdivision numbers of some families of graphs.
Źródło:: Discussiones Mathematicae Graph Theory; 2008, 28, 1; 109-119
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Domination numbers in graphs with removed edge or set of edges
Autorzy:: Lemańska, Magdalena
Powiązania:: https://bibliotekanauki.pl/articles/744295.pdf
Data publikacji:: 2005
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: connected domination number
weakly connected domination number
edge removal
Opis:: It is known that the removal of an edge from a graph G cannot decrease a domination number γ(G) and can increase it by at most one. Thus we can write that γ(G) ≤ γ(G-e) ≤ γ(G)+1 when an arbitrary edge e is removed. Here we present similar inequalities for the weakly connected domination number $γ_w$ and the connected domination number $γ_c$, i.e., we show that $γ_w(G) ≤ γ_w(G-e) ≤ γ_w(G)+1$ and $γ_c(G) ≤ γ_c(G-e) ≤ γ_c(G) + 2$ if G and G-e are connected. Additionally we show that $γ_w(G) ≤ γ_w(G-Eₚ) ≤ γ_w(G) + p - 1$ and $γ_c(G) ≤ γ_c(G -Eₚ) ≤ γ_c(G) + 2p - 2$ if G and G - Eₚ are connected and Eₚ = E(Hₚ) where Hₚ of order p is a connected subgraph of G.
Źródło:: Discussiones Mathematicae Graph Theory; 2005, 25, 1-2; 51-56
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Weakly connected domination critical graphs
Autorzy:: Lemańska, M.
Patyk, A.
Powiązania:: https://bibliotekanauki.pl/articles/255051.pdf
Data publikacji:: 2008
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: weakly connected domination number
tree
critical graphs
Opis:: A dominating set D ⊂ V(G) is a weakly connected dominating set in G if the subgraph G[D]w = (NG[D], Ew) weakly induced by D is connected, where Ew is the set of all edges with at least one vertex in D. The weakly connected domination number ϒw(G) of a graph G is the minimum cardinality among all weakly connected dominating sets in G. The graph is said to be weakly connected domination critical (ϒw-critical) if for each u, v ∈ V(G) with v not adjacent to u, ϒw(G + vu) < ϒw(G). Further, G is k- ϒw-critical if ϒw(G) = k and for each edge e ∉ E(G), ϒw(G + e) < k. In this paper we consider weakly connected domination critical graphs and give some properties of 3-ϒw,-critical graphs.
Źródło:: Opuscula Mathematica; 2008, 28, 3; 325-330
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

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